Signal generation using phase-shift based pre-coding

ABSTRACT

A phase-shift based pre-coding scheme used in a transmitting side and a receiving side that has less complexity than those of a space-time coding scheme, that can support various spatial multiplexing rates while maintaining the advantages of the phase-shift diversity scheme, that has less channel sensitivity than that of the pre-coding scheme, and that only requires a low capacity codebook is provided.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.11/754,873, filed May 29, 2007, currently pending, which pursuant to 35U.S.C. §119, claims the benefit of earlier filing date and right ofpriority to Provisional Application No. 60/803,340, filed on May 26,2006, Korea Korean Application No, 10-2006-65303, filed Jul. 12, 2006,and Korean Application No. 10-2006-97216, filed Oct. 2, 2006, thecontents of which are hereby incorporated by reference herein in theirentirety.

BACKGROUND

This disclosure relates to signal generation using phase-shift basedpre-coding.

Certain multi-carrier based wireless access techniques do not adequatelysupport mobile communication systems with various types of antennastructures.

The present inventors recognized certain shortcomings related to certainmulti-carrier based multiple antenna transmitting and/or receivingtechniques. Based upon such recognition, the following features havebeen conceived.

BRIEF DESCRIPTION

A phase-shift based pre-coding scheme used in a transmitting side and areceiving side that has less complexity than those of a space-timecoding scheme, that can support various spatial multiplexing rates whilemaintaining the advantages of the phase-shift diversity scheme, that hasless channel sensitivity than that of the pre-coding scheme, and thatonly requires a low capacity codebook has been conceived and providedherein. In particular, the matrix used for performing phase-shift basedpre-coding can be more easily expanded and implemented according to anychanges in the number of antennas being employed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an exemplary structure of a Multiple-Input Multiple-Output(MIMO) system using Orthogonal Frequency Division Multiplexing (OFDM).

FIG. 2 shows an exemplary structure of a transmitting side for amultiple antenna system using the cyclic delay diversity method.

FIG. 3 shows an exemplary structure of a transmitting side for amultiple antenna system using the phase-shift diversity method.

FIG. 4 is a graph showing examples of two types of phase-shift diversitymethods.

FIG. 5 shows an exemplary structure of a transmitting side for amultiple antenna system using a pre-coding method.

FIG. 6 shows the exemplary procedures in performing a phase-shiftdiversity method in a system having 4 antennas with a spatialmultiplexing rate of 2.

FIG. 7 shows an example of how a phase-shift based pre-coding method isapplied to the system of FIG. 6.

FIG. 8 shows an exemplary pre-coding matrix used in the phase-shiftbased pre-coding method for the system of FIG. 7.

FIG. 9 shows an exemplary block diagram of a transceiving apparatus thesupports the phase-shift based pre-coding method.

FIG. 10 shows an exemplary block diagram of a SCW OFDM transmitting unitwithin the radio communication unit of FIG. 9.

FIG. 11 shows an exemplary block diagram of a MCW OFDM transmitting unitwithin the radio communication unit of FIG. 9.

FIG. 12 is a graph showing a comparison in performance differences whenthe phase-shift pre-coding (PSP) method of the present inventiondisclosure and the spatial multiplexing (SM) method of the backgroundart are respectively applied to a ML (Minimum Likelihood) receiver and aMMSE (Minimum Mean Squared Error) receiver.

FIGS. 13 and 14 are graphs showing a comparison of the performancedifferences per coding rate for the phase-shift based pre-coding methodof the present disclosure and for the background art spatialmultiplexing method being applied to a MMSE (Minimum Mean Squared Error)receiver for a PedA (ITU Pedestrian A) fading channel environment and aTU (Typical Urban) fading channel environment.

FIGS. 15 through 17 are graphs showing a comparison of the performancedifferences when the present disclosure phase-shift based pre-codingmethod and the background art spatial multiplexing method are applied toa system employing SCW (Single CodeWord) and MCW (Multi CodeWord) in aPedA (ITU Pedestrian A) fading channel environment and a TU (TypicalUrban) fading channel environment.

FIG. 18 is a graph showing the performance differences in the caseswhere the spatial diversity method+cyclic delay diversity method isapplied, and the present disclosure phase-shift based pre-codingmethod+cyclic delay diversity method is applied to a MCS (Modulation andCoding Set) in a flat fading channel environment.

FIG. 19 shows an exemplary overview structure of downlink basebandsignal generation according to the present disclosure.

FIG. 20 shows the use of different delay values based on whetherfeedback information is used in accordance with one embodiment of thepresent invention.

DETAILED DESCRIPTION

Information communication services have become more popular and with theintroduction of various multimedia services and high quality services,there is an increased demand for enhanced wireless (radio) communicationservices. In order to actively meet such demands, the capacity and datatransmission reliability of the communication system should beincreased. To increase communication capacity in a wireless (radio)communication environment, one method would be to find newly usablebandwidth and another would be to improve the efficiency of givenresources. As some examples of the latter method, multiple antennatransmitting/receiving (transceiving) techniques are recently gainingattention and being actively developed, whereby a plurality of antennasare provided at the transceiver in order to obtain diversity gain byadditionally securing spatial domain for resource utilization, orincreasing transmission capacity by transmitting data in parallel viaeach antenna.

Among such multiple antenna transceiving techniques, an example would beMultiple-Input Multiple-Output (MIMO) system based on OrthogonalFrequency Division Multiplexing (OFDM), the general structure of whichwill now be explained with reference to FIG. 1.

At the transmitting side (or transmitter), a channel encoder 101 servesthe purpose of reducing the effects due to the channel or noise byattaching repetitive bits to the transmission data bits. A mapper 103changes the data bit information into data symbol information. Aserial-to-parallel converter 105 changes serial inputs into paralleloutputs for the purpose of MIMO processing on the data symbols. In thereceiving side (or receiver), a multiple antenna decoder 109, aparallel-to-serial converter 111, a demapper 113, and a channel decoder115 perform the opposite operations as those of the multiple antennaencoder 107, the serial-to-parallel converter 105, the mapper 103, andthe channel encoder 10 of the transmitting side described above.

In a multiple antenna OFDM system, various techniques are necessary toincrease transmission reliability. For example, space-time code (STC)techniques, cyclic delay diversity (CDD) techniques, antenna selection(AS) techniques, antenna hopping (AH) techniques, spatial multiplexing(SM) techniques, beam-forming (BF) techniques, pre-coding techniques,and the like may be employed. Among these techniques, some will beexplained in more detail hereafter.

The space-time code (STC) technique, for a multiple antenna environment,relates to continuously (sequentially) transmitting the same signal, butin case of repetitive transmissions, transmitting through differentantennas is performed, in order to obtain spatial diversity gain. Thefollowing matrix represents the most basic space-time code that is usedin a system with two transmit antennas.

$\frac{1}{\sqrt{S}}\begin{bmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}^{*}\end{bmatrix}$

In the above matrix, the rows represent antennas and the columnsrepresent time slots.

Such space-time code technique has some shortcoming. For example,respectively different forms of space-time codes are required accordingto how the antenna structure changes, the transmitting side andreceiving side have increased complexity because data symbols arerepeatedly transmitted through a plurality of time slots in order toobtain spatial diversity, and has respectively lower performancecompared to that of other closed-loop systems because data istransmitted without using feedback information. Table 1 below shows theneed for respectively different space-time codes according to antennastructures.

TABLE 1 Spatial Multiplexing # of Tx STC Scheme Rate antennas$\frac{1}{\sqrt{2}}\begin{bmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}\end{bmatrix}$ 1 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}$ 2 2${\frac{1}{\sqrt{2( {1 + r^{2}} )}}\begin{bmatrix}{S_{1} + {{jr} \cdot S_{4}}} & {{{r \cdot S_{2}} + S_{3}}\;} \\{S_{2} - {r \cdot S_{3}}} & {{{jr} \cdot S_{1}} + S_{4}}\end{bmatrix}},{r = {\sqrt{5} \pm {1/2}}}$ 2 2$\frac{1}{2}\begin{bmatrix}S_{1} & S_{2} & S_{3} & S_{4} \\S_{2}^{*} & {- S_{1}^{*}} & S_{4}^{*} & {- S_{3}^{*}} \\S_{3} & {- S_{4}} & {- S_{1}} & S_{2} \\S_{4}^{*} & S_{3}^{*} & {- S_{2}^{*}} & {- S_{1}^{*}}\end{bmatrix}$ 1 4 $\frac{1}{\sqrt{2}}\begin{bmatrix}S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0 \\0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*}\end{bmatrix}$ 1 4 $\frac{1}{2}\begin{bmatrix}S_{1} & {- S_{2}^{*}} & S_{5} & {- S_{6}^{*}} \\S_{2} & S_{1}^{*} & S_{6} & S_{5}^{*} \\S_{3} & {- S_{4}^{*}} & S_{7} & {- S_{8}^{*}} \\S_{4} & S_{3}^{*} & S_{8} & S_{7}^{*}\end{bmatrix}$ 2 4

Cyclic Delay Diversity (CDD) is a method in which frequency diversitygain is obtained at the receiving side, by using the antennas torespectively transmit signals with different delays or differentmagnitudes when transmitting OFDM signals in a system having multipletransceiving antennas.

FIG. 2 shows a general structure of a transmitting side of a multipleantenna system using the cyclic delay diversity method.

Upon separating and delivering the OFDM symbols to each antenna via aserial-to-parallel converter and a multiple antenna encoder, an InverseFast Fourier Transform (IFFT) for changing a frequency domain signalinto a time domain signal and a cyclic prefix (CP) for minimizinginterference between channels are added and transmitted to the receivingside. Here, the data sequence delivered to the first antenna istransmitted to the receiving side as is (i.e., without any changes),while the data sequence transmitted from other transmit antennas isdelayed in cyclic shift manner when compared to a first antenna.

Meanwhile, when such cyclic delay diversity scheme is implemented in thefrequency domain, the cyclic delay may be mathematically expressed as amultiplication of phase sequences.

Namely, as can be seen in FIG. 3, a particular phase sequence (e.g.,phase sequence 1˜phase sequence M) that has been set differently foreach antenna is multiplied to each data sequence in the frequencydomain, and upon performing IFFT (Inverse Fast Fourier Transform)processing, such can be transmitted to the receiving side. This isreferred to as a phase-shift diversity scheme.

By using the phase-shift diversity method, the flat fading channel maybe changed to a frequency selectivity channel, and frequency diversitygain or frequency scheduling gain may be obtained according to a cyclicdelay sample.

Namely, as can be seen in FIG. 4, in the phase-shift diversity scheme,when generating a phase sequence by using a relatively large valuecyclic delay sample, because the phase variation period is shortened(decreased), frequency selectivity is increased and as a result, thechannel codes may exploit frequency diversity gain. Such is typicallyused in so-called open-loop systems.

Also, when a small value cyclic delay is used, the phase variationperiod is lengthened (increased), and by using this in a closed-loopsystem, resources are allocated to the most satisfactory channel regionsuch that frequency scheduling gain can be obtained. Namely, as can beseen in FIG. 4, in the phase-shift diversity scheme, when a relativelysmall value cyclic delay is used for generating a phase sequence,certain sub-carrier regions of the flat fading channel result in anincrease in channel magnitude, while other sub-carrier regions result ina decrease in channel magnitude. In such case, for an OFDMA system thataccommodates multiple users, when a signal is transmitted through asub-carrier having an increased channel magnitude per user, thesignal-to-noise ratio can be increased.

However, despite some benefits of the above-described cyclic delaydiversity scheme or phase-shift diversity scheme, because the spatialmultiplexing rate is 1, the data transmission rate cannot be increasedas desired.

The pre-coding scheme may include a codebook based pre-coding methodused when there is a finite (or limited) amount of feedback informationin a closed-loop system and may include a method of performing feedbackupon quantization of channel information. Here, codebook basedpre-coding refers to obtaining signal-to-noise ratio (SNR) gain byfeeding back, to the transmitting side, an index of a pre-coding matrixthat is already known by both the transmitting side and the receivingside.

FIG. 5 depicts an exemplary structure of a transceiving side of amultiple antenna system using codebook based pre-coding. Here, thetransmitting side and the receiving side respectively have a finitepre-coding matrix (P₁˜P_(L)), and at the receiving side, channelinformation is used to feed back an optimal pre-coding matrix index (I),while at the transmitting side, a pre-coding matrix corresponding to thefed back index is applied to transmission data (x₁˜x_(Mt)).

Such codebook based pre-coding scheme is beneficial in that effectivedata transmission is possible due to feedback of the index. However,because a stable channel is necessary, such codebook based pre-codingmay not be fully appropriate for a mobile environment with severechannel changes. Also, some loss in the uplink transmission rate mayoccur due to the feedback overhead for the precoding matrix index.Additionally, because a codebook is needed in both the transmitting sideand the receiving side, increased memory usage may be required.

The present inventors recognized at least the above-described issues incertain data transmission, reception, and processing techniques formultiple antenna systems. Based upon such recognition, the followingfeatures have been conceived to address and/or to solve such issues.

This disclosure relates to and claims priority benefit of U.S.Provisional Application No. 60/803,340 (filed May, 26, 2006), KoreanPatent Application number 10-2006-0065303 (filed Jul. 12, 2006), andKorean Patent Application number 10-2006-0097216 (filed Oct. 2, 2006),which contents are specifically incorporated herein by reference.

The present disclosure relates to a phase-shift based pre-coding methodof a multiple antenna system using a plurality of sub-carriers, as wellas a generalized phase-shift based pre-coding method and a transceiverdevice supporting the same.

Hereafter, a phase-shift based pre-coding method will be explained withrespect to a 2-antenna system and a 4-antenna system, and a method offorming a generalized phase-shift based pre-coding matrix to beextendedly used for a system with an N_(t) number of (physical orvirtual) antennas will be described.

Phase-Shift Based Pre-Coding Method

A phase-shift based pre-coding matrix (P) proposed herein may begenerally expressed in the following manner:

$\begin{matrix}{P_{N_{i} \times R}^{k} = \begin{pmatrix}w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\\vdots & \vdots & \ddots & \vdots \\w_{N_{i},1}^{k} & w_{N_{i},2}^{k} & \ldots & w_{N_{i},R}^{k}\end{pmatrix}} & \lbrack {{Equation}\mspace{14mu} 1} \rbrack\end{matrix}$

Here, w_(i,j) ^(k), i=1, . . . , N_(t), j=1, . . . , R refers tomultiple complex weight values determined by sub-carrier index k, N_(t)refers to the number of (physical or virtual) transmit antennas, and Rrefers to a spatial multiplexing rate. If the phase-shift basedpre-coding matrix (P) is used in case of a physical antenna scheme, theN_(t) may be number of antenna port. Such sub-carrier index k can bereplaced by resource index including sub-band index. However, if P isused in case of a virtual antenna scheme, the N_(t) may be a spatialmultiplexing rate (i.e., R). Here, the multiple complex weight valuesmay be different according to the OFDM symbol being multiplied to theantenna and according to the corresponding sub-carrier index. Themultiple complex weight value may be determined according to at leastone of a channel condition and whether feedback information exists ornot.

The pre-coding matrix (P) of Equation 1 may be a unitary matrix forreducing the loss in channel capacity of a multiple antenna system.Here, to consider the conditions for forming a unitary matrix, thechannel capacity of a multiple antenna system may be expressed by thefollowing mathematical equation:

$\begin{matrix}{{C_{u}(H)} = {\log_{2}( {\det( {I_{N_{r}} + {\frac{S\; N\; R}{N}{HH}^{H}}} )} )}} & \lbrack {{Equation}\mspace{14mu} 2} \rbrack\end{matrix}$

Here, H refers to a multiple antenna channel matrix having a size ofN_(r)×N_(t), and N_(r) indicates the total number of receiving antennas.If a phase-shift based pre-coding matrix (P) is applied to the aboveEquation 2, the following may be obtained:

$\begin{matrix}{C_{precoding} = {\log_{2}( {\det( {I_{N_{r}} + {\frac{S\; N\; R}{N}{HPP}^{H}H^{H}}} )} )}} & \lbrack {{Equation}\mspace{14mu} 3} \rbrack\end{matrix}$

As shown in Equation 3, to minimize channel loss, PP^(H) needs to be anidentity matrix, thus the phase-shift based pre-coding matrix (P) shouldbe a unitary matrix such as the following:PP^(H)=I_(N),  [Equation 4]

In order for the phase-shift based pre-coding matrix (P) to be a unitarymatrix, two conditions should be satisfied. Namely, a power constraintand an orthogonality constraint should be simultaneously satisfied.Here, the power constraint refers to making the size of each column ofthe matrix to equal one (1), and the orthogonality constraint refers tomaking orthogonal characteristics between each column of the matrix tobe satisfied. The above matters may be expressed mathematically in thefollowing manner:

$\begin{matrix}\begin{matrix}{{{{w_{1,1}^{k}}^{2} + {w_{2,1}^{k}}^{2} + \ldots + {w_{N_{t},1}^{k}}^{2}} = 1},} \\{{{{w_{1,2}^{k}}^{2} + {w_{2,2}^{k}}^{2} + \ldots + {w_{N_{t},2}^{k}}^{2}} = 1},} \\\vdots \\{{{w_{1,R}^{k}}^{2} + {w_{2,R}^{k}}^{2} + \ldots + {w_{N_{t},R}^{k}}^{2}} = 1.}\end{matrix} & \lbrack {{Equation}\mspace{14mu} 5} \rbrack \\\begin{matrix}{{{w_{1,1}^{k*}w_{1,2}^{k}} + {w_{2,1}^{k*}w_{2,2}^{k}} + \ldots + {w_{N_{t},1}^{k*}w_{N_{t},2}^{k}}} = 0} \\{{{w_{1,1}^{k*}w_{1,3}^{k}} + {w_{2,1}^{k*}w_{2,3}^{k}} + \ldots + {w_{N_{t},1}^{k*}w_{N_{t},3}^{k}}} = 0} \\\vdots \\{{{w_{1,1}^{k*}w_{1,R}^{k}} + {w_{2,1}^{k*}w_{2,R}^{k}} + \ldots + {w_{N_{t},1}^{k*}w_{N_{t},R}^{k}}} = 0}\end{matrix} & \lbrack {{Equation}\mspace{14mu} 6} \rbrack\end{matrix}$

As an exemplary embodiment, a generalized equation for a 2×2 phase-shiftbased pre-coding matrix will be provided, and a mathematical expressionfor satisfying the above-described two conditions will be examined.Equation 7 shows a generalized expression of a phase-shift basedpre-coding matrix having a spatial diversity rate of 2 and having twotransmit antennas.

$\begin{matrix}{P_{2 \times 2}^{k} = \begin{pmatrix}{\alpha_{1}{\mathbb{e}}^{j\; k\;\theta_{1}}} & {\beta_{1}{\mathbb{e}}^{j\; k\;\theta_{2}}} \\{\beta_{2}{\mathbb{e}}^{j\; k\;\theta_{3}}} & {\alpha_{2}{\mathbb{e}}^{j\; k\;\theta_{4}}}\end{pmatrix}} & \lbrack {{Equation}\mspace{14mu} 7} \rbrack\end{matrix}$

Here, α_(i), β_(i) (i=1, 2) are real numbers, θ_(j) (j=1, 2, 3, 4)refers to phase values, and k is a sub-carrier index of the OFDM signal.In Equation 7, a relationship between a phase values B, (i=1, . . . , 4)of a frequency domain and a cyclic delay value τ_(i) (i=1, . . . , 4) ofa time domain is expressed as follows:θ_(i)=−2π/N _(fft)·τ_(i)where, N_(fft) denotes the number of subcarriers of the OFDM signal.

It can be understood that by those skilled in the art that thedescription thus far may be modified and altered in various ways withoutdeparting from the technical scope of the present disclosure.Accordingly, the technical scope should not be limited to that describedin the detailed description but should be embraced by the scope of theclaims. In order to implement such pre-coding matrix as a unitarymatrix, the power constraint of Equation 8 and the orthogonalityconstraint of Equation 9 should be satisfied.|α₁ e ^(jkθ) ¹ |²+|β₂ e ^(jkθ) ³ |²=1,|α₂ e ^(jkθ) ⁴ |²+|β₁ e ^(jkθ) ²|²=1  [Equation 8](α₁ e ^(jkθ) ¹ )*β₁ e ^(jkθ) ² +(β₂ e ^(jkθ) ³ )*α₂ e ^(jkθ) ⁴=0,  [Equation 9]

Here, the superscript (*) denotes a conjugate complex number. An exampleof a 2×2 phase-shift based pre-coding matrix that satisfies the aboveEquations 7 through 9 may be expressed as follows:

$\begin{matrix}{P_{2 \times 2}^{k} = {\frac{1}{\sqrt{2}}\begin{pmatrix}1 & {\mathbb{e}}^{j\; k\;\theta_{2}} \\{\mathbb{e}}^{j\; k\;\theta_{3}} & 1\end{pmatrix}}} & \lbrack {{Equation}\mspace{14mu} 10} \rbrack\end{matrix}$

Here, θ₂ and θ₃ have the relationship as shown in Equation 11 due to theorthogonality limitations.kθ ₃ =−kθ ₂+π  [Equation 11]

The pre-coding matrix may be stored in the form of a so-called codebook(or some equivalent type of precoding scheme, etc.) within a memory (orother type of storage device) of the transmitting side and the receivingside. Such codebook may include various types of pre-coding matricesformed by using a finite number of respectively different θ₂ values.Also, the θ₂ value may be appropriately set according to the channelenvironment, transmission rank, system bandwidth and whether or notfeedback information exists, and by setting the θ₂ value to berelatively small (e.g., 2 cyclic delay samples) if feedback informationis used or by setting the θ₂ value is set to be relatively high (e.g.,N_(fft)/N_(t) cyclic delay samples) if feedback information is not used,high frequency diversity gain may be obtained. FIG. 20 shows the use ofdifferent delay values based on whether feedback information is used.

Even when a phase-shift based pre-coding matrix such as that of Equation7 is formed, situations where the spatial multiplexing rate should beset to be small compared to the actual number of antennas according tothe channel environment may occur. In such case, in the phase-shiftbased pre-coding matrix formed in the above manner, a particular numberof columns corresponding to the current spatial multiplexing rate (i.e.,the spatial multiplexing rate that was made smaller) may be selected tore-generate a new phase-shift based pre-coding matrix. Namely, a newpre-coding matrix applied to the corresponding system need not always beformed whenever the spatial multiplexing rate changes. Instead, theinitially formed phase-shift based pre-coding matrix may be employed asis (i.e., without any changes), but one or more particular columns ofthe corresponding matrix may be selected to re-form the pre-codingmatrix.

As one such example, the pre-coding matrix of the above Equation 10assumes that the multiple antenna system has 2 transmit antennas with aspatial multiplexing rate of 2, but there may be some situations wherethe spatial multiplexing rate may actually be reduced to 1 for someparticular reason. In such case, pre-coding may be performed byselecting a particular column from the matrix of Equation 10 above, andif the second column is selected, the phase-shift based pre-codingmatrix is the same as that shown in Equation 12 below, and this becomesthe same as the cyclic delay diversity scheme for two transmit antennasof the conventional art.

$\begin{matrix}{P_{2 \times 1}^{k} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; k\;\theta_{2}} \\1\end{pmatrix}}} & \lbrack {{Equation}\mspace{14mu} 12} \rbrack\end{matrix}$

Here, this example assumes a system having 2 transmit antennas, but suchcan also be expanded for applicability to systems with 4 (or more)antennas. Namely, after generating a phase-shift based pre-coding matrixfor the case of 4 transmit antennas, pre-coding may be performed uponselecting one or more particular columns according to the changes in thespatial multiplexing rate.

As an example, FIG. 6 shows a case where the related art spatialmultiplexing and cyclic delay diversity are applied to a multipleantenna system having 4 transmit antennas and with a spatialmultiplexing rate of 2, while FIG. 7 shows a case where the phase-shiftbased pre-coding matrix of Equation 10 is applied to such a multipleantenna system.

According to FIG. 6, a 1^(st) sequence (S₁) and a 2^(nd) sequence (S₂)are delivered to the 1^(st) antenna and the 3^(rd) antenna, and a 1^(st)sequence (s₁e^(jk⊖1)) and 2^(nd) sequence (s₂e^(jk⊖1)) that have beenphase-shifted by using phase sequence of e^(jk⊖1) are delivered to the2^(nd) antenna and the 4^(th) antenna. Accordingly, it can be understoodthat the overall spatial multiplexing rate is 2.

On the other hand, according to FIG. 7, s₁+s₂e^(jk⊖2) is delivered tothe 1^(st) antenna, s₁e^(jk⊖1)+s₂e^(jk(⊖1+⊖2)) is delivered to the2^(nd) antenna, s₁e^(jk⊖3)+s₂ is delivered to the 3^(rd) antenna, ands₁e^(jk(⊖1+⊖3))+s₂e^(jk⊖1) delivered to the 4^(th) antenna. Thus, whencompared to the system of FIG. 6, the advantage of the pre-coding methodcan be obtained, and because cyclic delay (or phase-shift) can beperformed for 4 antennas by employing a uniform pre-coding matrix, theadvantage of the cyclic delay diversity scheme can also be obtained.

As one of example, the above-described phase-shift based pre-codingmatrices per different spatial multiplexing rates with respect to a2-antenna system and a 4-antenna system may be defined as follows.

TABLE 2 2-antenna system 4-antenna system Spatial Spatial SpatialSpatial multiplexing rate 1 multiplexing rate 2 multiplexing rate 1multiplexing rate 2 $\frac{1}{\sqrt{2}}\begin{pmatrix}1 \\e^{j\;\theta_{1}k}\end{pmatrix}$ $\frac{1}{\sqrt{2}}\begin{pmatrix}1 & {- e^{{- j}\;\theta_{1}k}} \\e^{j\;\theta_{1}k} & 1\end{pmatrix}$ $\frac{1}{\sqrt{4}}\begin{pmatrix}1 \\e^{j\;\theta_{1}k} \\e^{j\;\theta_{2}k} \\e^{j\;\theta_{3}k}\end{pmatrix}$ $\frac{1}{\sqrt{4}}\begin{pmatrix}1 & {- e^{{- j}\;\theta_{1}k}} \\e^{j\;\theta_{1}k} & 1 \\e^{j\;\theta_{2}k} & {- e^{{- j}\;\theta_{3}k}} \\e^{j\;\theta_{3}k} & {- e^{{- j}\;\theta_{2}k}}\end{pmatrix}$

Here, θ_(j) (j=1, 2, 3) refers to a phase angle according to the cyclicdelay value, and k refers to an OFDM sub-carrier index. In Table 2above, each pre-coding matrix of the four situations may be obtained byusing a particular portion of the pre-coding matrix with respect to amultiple antenna system having 4 antennas with a spatial multiplexingrate of 2 (as can be seen in FIG. 8). Accordingly, each pre-codingmatrix for such four situations need not be separately provided in acodebook, thus the memory resources in the transmitting side and thereceiving side may be conserved.

Referring to Table 2, it should be noted that when forming anappropriate phase-shift based pre-coding matrix according to a changedspatial multiplexing rate, a new column that satisfies the orthogonalconstraint to the other columns may be added.

Generalized Phase-Shift Based Pre-Coding Method

Thus far, the procedures of forming a phase-shift based pre-codingmatrix when there are 4 transmit antennas with a spatial multiplexingrate of 2 was explained, but the phase-shift based pre-coding method ofthe present disclosure may be expanded to a system having N_(t) antennas(here, N_(t) being a natural number of 2 or greater) with a spatialmultiplexing rate of R (here, R being a natural number of 1 or greater).Such may be obtained by using the same method described previously, andcan be generalized as the following Equation 13.

$\begin{matrix}{P_{N_{i} \times R}^{k} = {\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{N_{t}}k}\end{pmatrix}( U_{N_{t} \times R} )}} & \lbrack {{Equation}\mspace{14mu} 13} \rbrack\end{matrix}$

Here, at the right-side of the equal (=) symbol, the phase-shiftdiagonal matrix is combined with unitary matrix (U) used for aparticular purpose that satisfies the following condition: U_(N) _(t)_(×R) ^(H)×U_(N) _(t) _(×R)=I_(R×R). By multiplying the phase-shiftdiagonal matrix and some unitary matrix, the phase-shift based precodingthat satisfies both the power constraint and the orthogonal constraintmay be obtained. In addition, the phase-shift based precoding matrix canbe generated by multiplying one or more phase-shift diagonal matricesand/or one or more unitary matrices that can be obtained from feedbackinformation or downlink channel state information. In equation 13, thephase-shift diagonal matrix can be implemented by time domain cyclicdelay method if the k indicates sub-carrier index.

As an example of the unitary matrix (U), a specific pre-coding matrixfor obtaining signal-to-noise ratio (SNR) gain may be used, and inparticular, if Walsh codes are used for such pre-coding matrix, thephase-shift based pre-coding matrix generating equation may be asfollows:

$\begin{matrix}{P_{4 \times 4}^{k} = {\frac{1}{\sqrt{4}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}k} & 0 & 0 & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}k} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{j\theta}_{3}k} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{4}k}\end{pmatrix}\begin{pmatrix}1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1\end{pmatrix}}} & \lbrack {{Equation}\mspace{14mu} 14} \rbrack\end{matrix}$

In Equation 14, it is assumed that the system has 4 (physical orvirtual) transmit antennas with a spatial multiplexing rate of 4. Here,by appropriately re-forming the unitary matrix (U), a particulartransmit antenna may be selected (i.e., antenna selection) and/or theadjusting of spatial multiplexing rate (i.e., rate tuning) may bepossible.

The following Equation 15 shows an example of how the unitary matrix (U)may be re-formed in order to group 2 antennas of a system having 4antennas.

$\begin{matrix}{P_{4 \times 4}^{k} = {\frac{1}{\sqrt{4}}\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{1}k} & 0 & 0 & 0 \\0 & {\mathbb{e}}^{j\;\theta_{2}k} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{j\theta}_{3}k} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{4}k}\end{pmatrix}\begin{pmatrix}0 & 0 & 1 & 1 \\0 & 0 & 1 & {- 1} \\1 & 1 & 0 & 0 \\1 & {- 1} & 0 & 0\end{pmatrix}}} & \lbrack {{Equation}\mspace{14mu} 15} \rbrack\end{matrix}$

Also, the following Table 3 shows an exemplary method for re-forming theunitary matrix (U) to be appropriate for the corresponding multiplexingrate if the spatial multiplexing rate changes according to time, channelenvironment, and the like.

TABLE 3

Here, Table 3 shows some examples where column 1, columns 1˜2, andcolumns 1˜4 of the unitary is/are selected according to the multiplexingrate, but not meant to be limited to such. For example, if themultiplexing rate is 1, one of the 1^(st) through 4^(th) columns may beselected, if the multiplexing rate is 2, two particular columns (e.g.,one pair among the (1,2), (2,3), (3,4), (1,3), . . . , (2,4) pairs ofcolumns) may be selected, and if the multiplexing rate is 4, all columnsmay be selected.

Alternatively, the unitary matrix (U) may also be provided in codebookformat in the transmitting side and the receiving side. In such case,the transmitting side receives index information of the codebook asfeedback from the receiving side, then the appropriate unitary matrix(i.e., unitary precoding matrix in a codebook) corresponding to theindex is selected from its codebook, and then the above Equation 13 isused to form a phase-shift based pre-coding matrix.

Transceiving Apparatus Supporting a Phase-Shift Based Pre-Coding Method

FIG. 9 is a block diagram of an exemplary structure for a transceivingapparatus that supports the phase-shift based pre-coding method of theexemplary embodiments of the present invention. This exemplaryembodiment of the transceiving apparatus assumes that the unitary matrix(U) for forming the phase-shift based pre-coding matrix is provided incodebook format, but is not meant to be limited to such, as describedabove.

The transceiving apparatus may be comprised of an input unit (901) usedto select a desired function or receiving information, a display unit(903) used to show various information in using the transceivingapparatus, a memory unit (905) used to store various programs needed foroperating the transceiving apparatus and data to be transmitted to thereceiving side, a radio (wireless) communication unit (907) used toreceive signals and transmit data to the receiving side, a voiceprocessing unit (909) used to convert and amplify digital voice signalsinto analog voice signals for outputting through a speaker (SP) and toamplify the voice signals from a microphone (MIC) for converting intodigital signals, and a control unit (911) used to control the overalloperations of the transceiving apparatus.

The radio communication unit (907) will be explained in more detail asfollows. For reference, FIG. 10 is a block diagram showing an exemplarystructure of a SCW (Single Codeword) OFDM transmitter unit that isincluded in the radio communication unit (907), and FIG. 11 shows anexemplary structure of a MCW (Multiple Codeword) OFDM transmitter unit.Also, various receiver units that correspond to each transmitter unitalso exist and perform the opposite functions as those of thetransmitter units, but their detailed explanations will be omittedmerely for the sake of brevity.

In the SCW OFDM transmitter unit, a channel encoder (101) addsredundancy bits to prevent the transmit data from being distorted at(over) the channel, and channel encoding is performed by using errorcorrecting code codes (such as, turbo codes, LDPC codes, and the like).Thereafter, an interleaver (1020) performs interleaving through code bitparsing for minimizing losses due to instantaneous noise during the datatransmission procedure, and a mapper (1030) converts the interleaveddata bits into OFDM symbols. Such symbol mapping may be performedthrough phase modulation techniques (such as, QPSK, etc.) and amplitudemodulation techniques (such as, 16QAM, 8QAM, 4QAM, etc.). Thereafter,the OFDM symbols are processed through the pre-coder (1040) of thepresent invention disclosure, then processed through a sub-channelmodulator (not shown) and an Inverse Fast Fourier Transform (IFFT) unit(1050) are included into a carrier of the time domain. Upon processingthrough as filter unit (not shown) and an analog converter (1060),transmission via a radio channel is performed. Meanwhile, at the MCWOFDM transmitter unit, the only difference is that the OFDM symbols areprocessed through a channel encoder (111) and an interleaver (1120) in aparallel manner for each channel, otherwise, the remaining structuralelement (1130˜1160) may be the same (or similar).

The pre-coding matrix forming module (1041, 1141) determines a referencecolumn corresponding to a first sub-carrier in a particular pre-codingmatrix, and the remaining columns are determined by phase-shifting thereference column using a phase angle that is increased by a certain(consistent) amount. Here, a unitary matrix having a size of (number oftransmit antennas)×(spatial multiplexing rate) is employed to performpre-coding, and such unitary matrix is provided for each index of eachsub-carrier, whereby the unitary matrix with respect to the first indexis phase-shifted to obtain the unitary matrix of each remaining index.

Namely, the pre-coding matrix forming module (1041, 1141) selects acertain 1^(st) pre-coding matrix from a codebook previously stored inthe memory unit (905). A 2^(nd) pre-coding matrix with respect to asub-carrier or a sub-band of the 2^(nd) index is formed by applying aphase-shift of a certain size to the 1^(st) pre-coding matrix. Here, thesize of the shifted phase may be variously set according to the currentchannel condition and/or whether or not feedback information from thereceiving side exists. A 3^(rd) pre-coding matrix with respect to asub-carrier or a sub-band of the 3^(rd) index is formed by performing aphase-shift on the 2^(nd) pre-coding matrix. Namely, the formingprocedure of the 2^(nd) pre-coding matrix is repeated during theformation procedure of the 3^(rd) pre-coding matrix through the lastpre-coding matrix.

The pre-coding matrix re-forming module (1042, 1142) selects aparticular number of columns (in each pre-coding matrix formed by thepre-coding matrix forming module (1041, 1141)) that corresponds to thegiven spatial multiplexing rate and deletes the remaining columns inorder to re-form a pre-coding matrix. Here, a pre-coding matrixcomprised of the above-described selected columns may be newly formed.In selecting the particular column(s) of the pre-coding matrix, one ormore random columns may be selected or one or more particular columnsmay be selected according to pre-defined rules.

The pre-coding module (1043, 1143) performs pre-coding by applying OFDMsymbols for the corresponding sub-carrier into each pre-coding matrixdetermined in the above manner.

Generalized Phase-Shift Based Pre-Coding Method

Hereafter, the pre-coding matrix determining module (1041, 1141), thepre-coding matrix re-forming module (1042, 1142), and the pre-codingmodule (1043, 1143) according to another exemplary embodiment will beexplained.

The pre-coding matrix determining module (1041, 1141) selects aparticular unitary matrix (U) by referring to the unitary matrix indexthat was fed back from the receiving side or by using a pre-definedmatrix, and the selected unitary matrix (U) is applied to the aboveEquation 13 to determine a phase-shift based pre-coding matrix (P).Here, the phase-shift value of the former matrix of Equation 13 shouldbe previously set.

There may be situations where the spatial multiplexing rate needs to beadjusted due to changes in channel environment or where datatransmission needs to be performed by selecting a particular antennaamong multiple transmit antennas due to various reasons. In such case,when a change in spatial multiplexing rate and/or a change in the numberof antennas is informed from the control unit (911), the pre-codingre-forming module (1042, 1142) searches for a unitary matrix (U) that isappropriate for the corresponding situation or a previously selectedunitary matrix (U) is re-formed to be appropriate for the correspondingsituation. In the former case, there is the advantage that the desiredphase-shift based pre-coding matrix can be quickly obtained because aseparate re-forming procedure is not necessary, but there is thedisadvantage that memory usage increases because a codebook that is beused for various situations needs to be provided. Also, in the lattercase, processing load is created due to the re-forming procedures, butthe codebook capacity can be reduced. The unitary matrix re-formingprocedure according to spatial multiplexing rate changes or changes inthe number of transmit antennas was explained previously with respect toEquation 14 and Table 3.

The pre-coding module (1043, 1143) performs pre-coding by applying theOFDM symbols (with respect to the corresponding sub-carrier or sub-band)to the phase-shift based pre-coding matrix determined in the abovemanner.

The control unit (911) informs the pre-coding matrix re-forming module(1042, 1142) about various information (such as, the changed spatialmultiplexing rate, the changed total number of antennas to be used,etc.) that is used for re-forming the pre-coding matrix.

The transceiving apparatus according to the present invention disclosuremay be used in so-called Personal Digital Assistants (PDAs), cellularphones, Personal Communication Service (PCS) phones, GSM phones, WCDMAphones, Mobile Broadband System (MBS) phones, and the like.

By applying both the phase-shift based pre-coding method describedherein and the spatial multiplexing method of the background art to amultiple antenna OFDM open loop system that does not employ feedbackinformation, the differences in performance of these two methods will beexplained with reference to some experimental test results. Table 4shows the parameters that were applied to the system for thisexperimental test.

TABLE 4 Parameter Parameter value # of sub-carriers 512 # of guardcarriers 106 (left), 105 (right) # of pilots 28 (perfect channelestimation) MIMO scheme Spatial Multiplexing (SM) and phase- shiftpre-coding (PSP) MIMO receiver MMSE (Minimum Mean Squared Error), ML(Minimum Likelihood) Bandwidth 7.68 MHz Carrier frequency 2 GHz Channelmodel Flat, Ped-A (ITU Pedestrian A), TU (Typical Urban), Mobility: 30km/h, 250 km/h # of OFDM symbols 8 (localized) per frame MCS (Modulationand QPSK (R = ¼, R = ⅓. R = ½, R = ¾) Coding Set) Channel coding 3GPPTurbo (Max-long-MAP), 8 Iterations # of transmit antennas 2 # of receiveantennas 2 Antenna correlation (0%, 0%)

FIG. 12 is a graph showing a comparison in performance differences whenthe phase-shift-based pre-coding (PSP) method of the present inventiondisclosure and the spatial multiplexing (SM) method of the backgroundart are respectively applied to a ML (Minimum Likelihood) receiver and aMMSE (Minimum Mean Squared Error) receiver.

As depicted, in a system that applies the PSP method, a larger gain cangenerally be obtained when compared to the background art spatialmultiplexing method. More specifically, in the ML receiver, the PSPmethod results in slightly more gain when compared to the SM method, butin the MMSE receiver, it can be seen that a larger gain may be obtainedwith the PSP method as the signal-to-noise ration (SNR) increases.

FIGS. 13 and 14 are graphs showing a comparison of the performancedifferences per coding rate for the phase-shift based pre-coding methodof the present invention disclosure and for the background art spatialmultiplexing method being applied to a MMSE (Minimum Mean Squared Error)receiver for a Ped-A (ITU Pedestrian A) fading channel environment and aTU (Typical Urban) fading channel environment.

As depicted, it can be seen that on the Ped-A (ITU Pedestrian A) fadingchannel environment and the TU (Typical Urban) fading channelenvironment, the PSP method can obtain a large gain by increasingfrequency selectivity while decreasing coding rate (R=⅓, R=¼).

FIGS. 15 through 17 are graphs showing a comparison of the performancedifferences when the present invention disclosure phase-shift basedpre-coding method and the background art spatial multiplexing method areapplied to a system employing SCW (Single Codeword) and MCW (MultipleCodeword) in a Ped-A (ITU Pedestrian A) fading channel environment and aTU (Typical Urban) fading channel environment.

In general, when the spatial multiplexing method is applied to SCW,higher performance compared to that of MCW is achieved, because thechannel code can additionally obtain spatial diversity gain and canobtain coding gain due to an increase in codeword length, but has thedrawback that reception requires a high degree of complexity. Asdepicted, in a system with the spatial multiplexing method appliedthereto, there is a large difference in performance between SCW and MCW.However, if the present invention disclosure phase-shift basedpre-coding method is applied, a larger gain compared to that of the SCWof a system with the spatial multiplexing method applied thereto can beobtained. Namely, as depicted, a much larger gain is generated whenphase-shift based pre-coding is applied in comparison to when thebackground art spatial multiplexing method is applied to MCW, andalthough a respectively smaller gain is generated compared to when SCWis applied, but it is clear that an improvement in performance isachieved.

FIG. 18 is a graph showing the performance differences in the caseswhere the spatial diversity method+cyclic delay diversity method isapplied, and the present invention disclosure phase-shift basedpre-coding method+cyclic delay diversity method is applied to a MCS(Modulation and Coding Set) in a flat fading channel environment.

As depicted, for all coding rates (R=½, ⅓, ¼), it can be seen thatsuperior performance is achieved when the present invention disclosurephase-shift based pre-coding method+cyclic delay diversity method isapplied, compared to when the background art spatial diversitymethod+cyclic delay diversity method is applied.

As for some exemplary effects of the present invention disclosure thatemploys the phase-shift based pre-coding method, when compared to thespace-time coding method, the degree of complexity of the transceiver isrelatively low, the advantages of the phase-shift diversity scheme ismaintained while supporting various spatial multiplexing rates. Comparedto the pre-coding method, relatively less channel sensitivity and theneed for a relatively small capacity codebook can be expected.Furthermore, by using a generalized phase-shift based pre-coding matrix,phase-shift based pre-coding can be easily expanded and appliedregardless of the number of transmit antennas in the system.

FIG. 19 shows an exemplary overview structure related to downlinkbaseband signal generation according to the present disclosure.

As for industrial applicability, the features and aspects describedherein are related to and can be implemented for various types of radiocommunication techniques. Some non-limiting examples may includebroadband wireless air interface techniques, Multiple-InputMultiple-Output (MIMO) techniques, so-called 3.5G or 4G systems designedto provide higher data rates and IP-based data services, etc. and/orvarious radio communication standards, such as, but not limited to,WCDMA, 3GPP, 3GPP2, OFDM, OFDMA, HSDPA, UMTS, OMA, IEEE 802.11n, IEEE802.16, etc.

As such, at least some of the features described herein are applicableto such standards that have been developed or that are continuing toevolve. Also, at least some of the features described herein may beimplemented in various types of devices (e.g., mobile phones, wirelesscommunication terminals, user equipment (UE), radio communicationprotocol entities, etc.) in terms of hardware, software, or someappropriate combination thereof.

Any reference in this specification to “one embodiment,” “anembodiment,” “example embodiment,” etc., means that a particularfeature, structure, or characteristic described in connection with theembodiment is included in at least one embodiment of the invention. Theappearances of such phrases in various places in the specification arenot necessarily all referring to the same embodiment. Further, when aparticular feature, structure, or characteristic is described inconnection with any embodiment, it is submitted that it is within thepurview of one skilled in the art to affect such feature, structure, orcharacteristic in connection with other ones of the embodiments.

Although embodiments have been described with reference to a number ofillustrative embodiments thereof, it should be understood that numerousother modifications and embodiments can be devised by those skilled inthe art that will fall within the scope of the principles of thisdisclosure. More particularly, various variations and modifications arepossible in the component parts and/or arrangements of the subjectcombination arrangement within the scope of the disclosure, the drawingsand the appended claims. In addition to variations and modifications inthe component parts and/or arrangements, alternative uses will also beapparent to those skilled in the art.

1. A method for transmitting a signal by a transmitter via N_(t)antennas in a multiple antenna system using multiple subcarriers, themethod comprising: acquiring a plurality of modulation symbol streams bymodulating a transmission signal; phase-shift based precoding theplurality of modulation symbol streams using a matrix of D*U to outputN_(t) symbol streams; and transmitting the ‘N_(t)’ symbol streams viathe N_(t) antennas, wherein D is a diagonal matrix and U is a unitarymatrix, wherein U and D are determined such that the plurality ofmodulation symbol streams are cyclically delayed with a unit of a firstdelay value when feedback information from a receiver is not used,wherein U and D are determined such that the plurality of modulationsymbol streams are cyclically delayed with a unit of a second delayvalue, when the feedback information from the receiver is used, andwherein the first delay value is larger than the second delay value. 2.The method of claim 1, wherein D is determined based on a multiplexingrate.
 3. The method of claim 1, wherein D has different phase shiftangles for each row of the diagonal matrix.
 4. The method of claim 1,wherein U is determined based on a multiplexing rate.
 5. The method ofclaim 1, wherein U is predetermined in a form of a codebook.
 6. Themethod of claim 1, wherein: the phase-shift based precoding is performedin a form of D*U*X when a number of the multiple antennas is 2 and amultiplexing rate is 2; a number of the plurality of modulation symbolstreams is m; and X is an m*1 matrix consisting of the plurality ofmodulation symbol streams.
 7. The method of claim 1, wherein: U ispredetermined based on a value of N_(t) and a multiplexing rate (R); andphase angles of D are linearly increased according to a frequency index.8. The method of claim 7, wherein the matrix of D*U is represented as:${\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{1}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{j\;\theta_{2}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{j\;\theta_{N_{t}}k}\end{pmatrix}( U_{N_{t \times R}} )},$ where U has adimension of Nt*R and ‘k’ represents the frequency index.
 9. A methodfor receiving a signal by a receiver in a multiple antenna system usingmultiple subcarriers, the method comprising: receiving the signaltransmitted from a transmitter via N_(t) antennas; performing a functionthat is opposite to a phase-shift based precoding on the received signalusing a matrix of D*U; and demodulating the signal on which the oppositefunction was performed, wherein D is a diagonal matrix and U is aunitary matrix, wherein U and D are the same matrices determined at thetransmitter such that a plurality of modulation symbol streams arecyclically delayed with a unit of a first delay value, when feedbackinformation from the receiver is not used, wherein U and D are the samematrices determined at the transmitter such that the plurality ofmodulation symbol streams are cyclically delayed with a unit of a seconddelay value, when the feedback information from the receiver is used,and wherein the first delay value is larger than the second delay value.10. The method of claim 9, wherein D is determined based on amultiplexing rate.
 11. The method of claim 9, wherein U is determinedbased on a multiplexing rate.
 12. The method of claim 9, wherein U ispredetermined within a codebook.
 13. The method of claim 9, wherein: Uis predetermined based on a value of N_(t) and a multiplexing rate (R);and phase angles of D are linearly increased according to a frequencyindex.
 14. The method of claim 13, wherein the matrix of D*U isrepresented as: ${\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{1}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{j\;\theta_{2}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{j\;\theta_{N_{t}}k}\end{pmatrix}( U_{N_{t \times R}} )},$ where U has adimension of Nt*R and ‘k’ represents the frequency index.
 15. Anapparatus for transmitting a signal via N_(t) antennas in a multipleantenna system using multiple subcarriers, the apparatus comprising: amapper acquiring a plurality of modulation symbol streams by modulatinga transmission signal; and a precoder performing a phase-shift basedprecoding on the plurality of modulation symbol streams using a matrixof D*U to output N_(t) symbol streams, wherein D is a diagonal matrixand U is a unitary matrix, wherein U and D are determined such that theplurality of modulation symbol streams are cyclically delayed with aunit of a first delay value when feedback information from a receiver isnot used, wherein U and D are determined such that the plurality ofmodulation symbol streams are cyclically delayed with a unit of a seconddelay value, when the feedback information from the receiver is used,and wherein the first delay value is larger than the second delay value.16. The apparatus of claim 15, wherein D is determined based on amultiplexing rate.
 17. The apparatus of claim 15, wherein D hasdifferent phase shift angles for each row of the diagonal matrix. 18.The apparatus of claim 15, wherein U is determined based on amultiplexing rate.
 19. The apparatus of claim 15, further comprising: amemory unit storing U in a form of a codebook.
 20. The apparatus ofclaim 15, wherein: U is predetermined based on a value of N_(t) and amultiplexing rate (R); and phase angles of D are linearly increasedaccording to a frequency index.
 21. The apparatus of claim 20, whereinthe matrix of D*U is represented as: ${\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{1}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{j\;\theta_{2}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{j\;\theta_{N_{t}}k}\end{pmatrix}( U_{N_{t \times R}} )},$ where U has adimension of Nt*R and ‘k’ represents the frequency index.
 22. Anapparatus for receiving a signal in a multiple antenna system usingmultiple subcarriers, the apparatus comprising: one or more antennas forreceiving the signal transmitted from a transmitter via N_(t) antennas;a precoder performing a function that is opposite to a phase-shift basedprecoding on the received signal using a matrix of D*U; and a demapperdemodulating the signal on which the opposite function was performed,wherein D is a diagonal matrix and U is a unitary matrix, wherein U andD are the same matrices determined at the transmitter such that aplurality of modulation symbol streams are cyclically delayed with aunit of a first delay value, when feedback information from theapparatus is not used, wherein U and D are the same matrices determinedat the transmitter such that the plurality of modulation symbol streamsare cyclically delayed with a unit of a second delay value, when thefeedback information from the apparatus is used, and wherein the firstdelay value is larger than the second delay value.
 23. The apparatus ofclaim 22, wherein D is determined based on a multiplexing rate.
 24. Theapparatus of claim 22, wherein U is determined based on a multiplexingrate.
 25. The apparatus of claim 22, further comprising: a memory unitstoring U in a form of a codebook.
 26. The apparatus of claim 22,wherein: U is predetermined based on a value of N_(t) and a multiplexingrate (R); and phase angles D are linearly increased according to afrequency index.
 27. The apparatus of claim 26, wherein the matrix ofD*U is represented as: ${\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{1}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{j\;\theta_{2}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{j\;\theta_{N_{t}}k}\end{pmatrix}( U_{N_{t \times R}} )},$ where U has adimension of Nt*R and ‘k’ represents the frequency index.